[go: up one dir, main page]

login
A040702
Continued fraction for sqrt(730).
4
27, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54
OFFSET
0,1
FORMULA
From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 54 for n >= 1.
G.f.: 27*(1+x)/(1-x).
E.g.f.: 54*exp(x) - 27.
a(n) = 27*A040000(n) = 9*A040006(n) = 3*A040072(n). (End)
EXAMPLE
27 + 1/(54 + 1/(54 + 1/(54 + 1/(54 + ...)))) = sqrt(730).
MAPLE
with(numtheory): Digits := 300: convert(evalf(sqrt(730)), confrac);
CROSSREFS
Cf. A042404/A042405 (convergents).
Sequence in context: A255364 A082915 A183032 * A305548 A306824 A043323
KEYWORD
nonn,cofr,easy
STATUS
approved